Virtual Angular-Domain Channel Estimation for FDD Based Massive MIMO Systems With Partial Orthogonal Pilot Design

This article proposes a virtual angular-domain channel estimation scheme for massive multiple-input multiple-output systems operating in frequency division duplex (FDD) mode. Different from the conventional scheme where orthogonal pilots are transmitted on different antennas, we propose to transfer the channel estimation problem to the virtual angular domain and utilize the channel sparsity to reduce the training and feedback overhead. An orthogonal matching pursuit with Gram-Schmidt orthogonalization algorithm is proposed to construct the unitary transformation between the spatial domain and the virtual angular domain, which achieves higher sparsity than the existing approaches. Furthermore, we propose to estimate the downlink (DL) dominant angular set, which captures most of the channel power with only a few elements, by utilizing the directional reciprocity of FDD systems, where a calibration algorithm is introduced to handle the different wavelengths of uplink and DL transmissions. Based on the estimated dominant sets, we introduce a partial orthogonal criterion for virtual angular-domain pilot design and further propose two pilot assignment algorithms which minimize pilot overhead and pilot-reuse interference, respectively. Theoretical analyses on pilot overhead and the mean square error (MSE) performance are also presented. Simulation results demonstrate that our proposed virtual angular-domain channel estimation scheme provides excellent MSE performance with much reduced pilot overhead and, consequently, enjoys much larger per-user achievable rate in comparison to the conventional schemes.